Apologies for the misunderstanding earlier. Let's correct that.

The question is asking for the principal value of \(\tan^{-1}(-44)\).

### Solution:

The arctangent function \(\tan^{-1}(x)\) gives an angle \(\theta\) such that:
\[
-\frac{\pi}{2} < \theta < \frac{\pi}{2}
\]
for which \(\tan(\theta) = x\).

1. **Calculate the angle for \(\tan^{-1}(-44)\):**

   - Since \( \tan^{-1}(x) \) is negative, the angle will be in the fourth quadrant.
   - Typically, a very large negative tangent value like \(-44\) indicates an angle close to \(-\frac{\pi}{2}\) (or \(-90^\circ\)).

2. **Determine the principal value:**

   To find the angle, using a calculator:
   \[
   \theta = \tan^{-1}(-44)
   \]
   The arctangent of \(-44\) yields an angle close to \(-\frac{\pi}{2}\).

   In degrees, \(\theta\) will be close to \(-88.7^\circ\), which fits with the fourth quadrant angle.

Thus, the correct principal value of \(\tan^{-1}(-44)\) is indeed **-88.7°**.

### Relative Questions:
1. How does the value of tangent affect the quadrant in which the angle lies?
2. What is the relationship between \(\tan^{-1}(x)\) and the sign of \(x\)?
3. How would you find the principal value of \(\tan^{-1}(0.5)\)?
4. Why is \(\tan^{-1}(x)\) restricted to \(-90^\circ\) to \(90^\circ\)?
5. What happens if \(x\) in \(\tan^{-1}(x)\) is a very large positive number?

### Tip:
When evaluating \(\tan^{-1}(x)\) for very large negative or positive values of \(x\), expect the angle to be very close to \(-90^\circ\) or \(90^\circ\), respectively.

Explore the principal value of the arctangent function \( \tan^{-1}(-44) \) and understand how to find it. This problem involves trigonometric concepts and calculations in the fourth quadrant. Suitable for high school students learning trigonometry.

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